Theme Essential Question: How can you use numerical and algebraic expressions, equations, and inequalities to solve real life mathematical problems?
Essential Question:
Can students determine whether a number is a solution of an equation?
Can students determine whether a number is a solution of an inequality?
Standards
6.EE.5 Reason about and solve one-variable equations and inequalities. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
Objectives
Students will determine whether a number is a solution of an equation.
Students will determine whether a number is a solution of an inequality.
Reflections and/or Comments from your PCSSD 6th Grade Curriculum Team (Taken from Ohio Department of Education: http://education.ohio.gov/GD/DocumentManagement/DocumentDownload.aspx?DocumentID=106873)
The skill of solving an equation must be developed conceptually before it is developed procedurally. This means that students should be thinking about what numbers could possibly be a solution to the equation before solving the equation. For example, in the equation x + 21 = 32 students know that 21 + 9 = 30 therefore the solution must be 2 more than 9 or 11, so x = 11. Provide multiple situations in which students must determine if a single value is required as a solution, or if the situation allows for multiple solutions. This creates the need for both types of equations (single solution for the situation) and inequalities (multiple solutions for the situation). When working with inequalities, provide situations in which the solution is not limited to the set of positive whole numbers but includes rational numbers. This is a good way to practice fractional numbers.
Background Information
Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials.
Beginning experiences in solving equations should require students to understand the meaning of the equation as well as the question being asked. Solving equations using reasoning and prior knowledge should be required of students to allow them to develop effective strategies such as using reasoning, fact families, and inverse operations. Students may use balance models in representing and solving equations and inequalities.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Vocabulary
Math
Equation Inequality Solution of an inequality Symbols for: less than, greater than, less than or equal to, greater than or equal to Solution of an equation Variable Solution of an inequality Equals sign
Suggested Activities On Core Mathematics
Solutions of Equations Lesson 57 p113-114
Solutions of Inequalities Lesson 58 p115-116
Mastering the Common Core ABC
Nothing completely matching
Teaching the Common Core Math Standards with Hands-On Activities Grades 6-8
Three in a Row p39
Extention would be to have the class create there own Equations and Inequalities sheet to trade amoung classes.
Gizmos
None at this time
JBHM
Nothing specific
Glenco
6th 1-7a, 9-4b,
7th 1-5a, p153, 4-4a
Highly Recommended: The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions. Tasks that illustrate content standard 6.EE.5:
Inequaltities Dates: 1/22-1/25
Theme Essential Question:
How can you use numerical and algebraic expressions, equations, and inequalities to solve real life mathematical problems?
Essential Question:
Standards
Objectives
Reflections and/or Comments from your PCSSD 6th Grade Curriculum Team
(Taken from Ohio Department of Education: http://education.ohio.gov/GD/DocumentManagement/DocumentDownload.aspx?DocumentID=106873)
The skill of solving an equation must be developed conceptually before it is developed procedurally. This means that students should be thinking about what numbers could possibly be a solution to the equation before solving the equation. For example, in the equation x + 21 = 32 students know that 21 + 9 = 30 therefore the solution must be 2 more than 9 or 11, so x = 11. Provide multiple situations in which students must determine if a single value is required as a solution, or if the situation allows for multiple solutions. This creates the need for both types of equations (single solution for the situation) and inequalities (multiple solutions for the situation). When working with inequalities, provide situations in which the solution is not limited to the set of positive whole numbers but includes rational numbers. This is a good way to practice fractional numbers.
Background Information
Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials.
Assessment
Product
Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary
Inequality
Solution of an inequality
Symbols for: less than, greater than, less than or equal to, greater than or equal to
Solution of an equation
Variable
Solution of an inequality
Equals sign
Suggested Activities
On Core Mathematics
- Solutions of Equations Lesson 57 p113-114
- Solutions of Inequalities Lesson 58 p115-116
Mastering the Common Core ABC- Nothing completely matching
Teaching the Common Core Math Standards with Hands-On Activities Grades 6-8- Three in a Row p39
- Extention would be to have the class create there own Equations and Inequalities sheet to trade amoung classes.
Gizmos- None at this time
JBHM- Nothing specific
Glenco- 6th 1-7a, 9-4b,
- 7th 1-5a, p153, 4-4a
Highly Recommended: The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.Tasks that illustrate content standard 6.EE.5:
- Log Ride http://illustrativemathematics.org/illustrations/673
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